Adaptive Quantum State Tomography Using Machine Learning

The reconstruction of quantum states from experimental measurement data is essential to characterize a quantum state prepared in a noisy, imperfect experimental setup. A quantum state is mathematically fully described by its density matrix. Quantum state tomography is the process of reconstructing the density matrix of a quantum system based on a series of experimental measurements.

Traditional quantum state tomography reconstructs a system's density matrix using measurements in a fixed set of bases, using numerical methods such as maximum likelihood estimation. While a complete set of measurement bases scales exponentially with the size of the quantum system, there is evidence that an accurate approximate density matrix reconstruction can be obtained from measurements in a subset of bases. Here we employ machine learning techniques to dynamically select the most informative measurement at each step. Instead of following a predetermined sequence, we aim to adapt the relevant measurement bases in real time based on the outcomes of previous measurements.

In this adaptive approach, machine learning models continuously update the measurement strategy to maximize information gain, thereby reducing uncertainty in the reconstructed state. This is particularly advantageous for systems involving multiple particles, where the complexity of the density matrix increases dramatically. By focusing on those measurements most likely to improve the fidelity of the state reconstruction, the method has the potential to be both more efficient and more accurate than traditional, static protocols. Practical implementation of such techniques must account for real-world issues like noise and experimental imperfections while maintaining the computational speed required for real-time decisions.